How to bend two parts of a flat objects on two different axis?
You could go with the Bend, using limits and Axis/Orientation Empties in the modifiers, but IMO, you would get finer control over the curves using Curve modifiers throughout?

Excluding the flat region from the circular curve modifier

In order to keep the end of the folded-over region flat, it must remain unaffected either by the mapping of the entire object into the curve, or the subsequent deformation. The first is achieved by arranging origins. 


The circle's origin is placed at its first vertex, and at World 0.
The object's origin is placed at the center of its X dimension, at its minimum Z
The object is then translated in X (effectively rotating it around the circle under deformation) until the part of the mesh we want to remain stationary is directly above the circle's origin.




The second is achieved by weight painting:


The circle Curve modifier (deforming in X) is aimed at a vertex group - it does not affect the unweighted region:




The bottom is curved, the top remains flat, and in place.

Adding a second curve modifier to fold over a section.

The folding curve modifier deforms in Z, its curve can be anywhere you like in X, but here shown with its origin in the same place as the circle curve.



You could flatten more or less of the flap with weight-painting.